Southwest Airlines says it will issue refunds to customers who were charged multiple reservation charges as a result of a glitch with a Facebook promotion.

A one-day Southwest promotion to celebrate the airline's reaching the 3 million Facebook fan mark was supposed to give customers who purchased tickets on Friday a 50 percent discount on certain flights. However, a glitch with the Southwest reservation system caused customers' credit and debit cards to be billed multiple times for a single purchase, in some cases 20 or more times, according to hundreds of Facebook and Twitter posts.

The airline said on its Facebook page Saturday that "website performance issues" were to blame for the billing issues and that it was working to identify duplicate charges.

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"We realize that some customers were charged more than once for the same reservation and we want to ensure you that we have all hands on deck, actively working to process refunds for any duplicate charges incurred," the airline said. "It is our goal to resolve this issue as quickly as possible and minimize any inconvenience."

The airline said it had brought in additional staff to help identify duplications and process refunds. Southwest also said it would reimburse overdraft charges suffered by debit card customers.